SPDEs driven by space-time white noise in high dimensions: absolute continuity of the law and convergence of solutions |
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| Authors: | TS Zhang WA Zheng |
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| Institution: | 1. Department of Mathematics , University of Manchester , Oxford Road, Manchester MPL, 13 9, England, UK;2. Department of Mathematics , University of California at Irvine , 92697, Irvine, CA, USA |
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| Abstract: | In this paper, we consider stochastic partial differential equations driven by space-time white noise in high dimensions. We prove, under reasonable conditions, that the law of the solution admits a density with respect to Lebesgue measure. The stability of the equation, as the higher order differential operator tends to zero, is also studied in the paper. |
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| Keywords: | Malliavin Calculus Stochastic partial differential equations Semigroups Eigenvalues and Eigenvectors 60H07 60H15 60G20 60G60 |
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